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Context-specific independence in graphical log-linear models
Authors:Henrik Nyman  Johan Pensar  Timo Koski  Jukka Corander
Institution:1.Department of Mathematics and Statistics,?bo Akademi University,Turku,Finland;2.Department of Mathematics,KTH Royal Institute of Technology,Stockholm,Sweden;3.Department of Mathematics and Statistics,University of Helsinki,Helsinki,Finland
Abstract:Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific independence. However, parameter estimation is often simpler under a direct parameterization, provided that the model enjoys certain decomposability properties. Here we introduce a cyclical projection algorithm for obtaining maximum likelihood estimates of log-linear parameters under an arbitrary context-specific graphical log-linear model, which needs not satisfy criteria of decomposability. We illustrate that lifting the restriction of decomposability makes the models more expressive, such that additional context-specific independencies embedded in real data can be identified. It is also shown how a context-specific graphical model can correspond to a non-hierarchical log-linear parameterization with a concise interpretation. This observation can pave way to further development of non-hierarchical log-linear models, which have been largely neglected due to their believed lack of interpretability.
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